Free convection of magnetic nanofluid considering MFD viscosity effect

•MFD viscosity effect on MHD nanofluid heat transfer is investigated.•CVFEM is applied to solve the governing equations.•Nuave has a reverse relationship with δ⁎ , Ha.•Effect of MFD viscosity is more sensible for high Ra.

In this study effect of magnetic field dependent (MFD) viscosity on free convection heat transfer of nanofluid in an enclosure is investigated. The bottom wall has constant flux heating element. Single phase nanofluid model is utilized considering Brownian motion. Control Volume based Finite Element Method is applied to simulate this problem. The effects of viscosity parameter, Hartmann number and Rayleigh number on hydrothermal behavior have been examined. Results show that Nusselt number is an increasing function of Rayleigh number and volume fraction of nanoparticle while it is a decreasing function of viscosity parameter and Hartmann number. Also it can be found that reduction of Nusselt number due to MFD viscosity effect are more sensible for high Rayleigh number and low Hartmann number.